Problem: Simplify the following expression: $ r = \dfrac{-4z}{2z - 8} + \dfrac{-2}{9} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-4z}{2z - 8} \times \dfrac{9}{9} = \dfrac{-36z}{18z - 72} $ Multiply the second expression by $\dfrac{2z - 8}{2z - 8}$ $ \dfrac{-2}{9} \times \dfrac{2z - 8}{2z - 8} = \dfrac{-4z + 16}{18z - 72} $ Therefore $ r = \dfrac{-36z}{18z - 72} + \dfrac{-4z + 16}{18z - 72} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-36z - 4z + 16}{18z - 72} $ $r = \dfrac{-40z + 16}{18z - 72}$ Simplify the expression by dividing the numerator and denominator by 2: $r = \dfrac{-20z + 8}{9z - 36}$